“In five years, the world will be completely different in terms of education”
You are active in Hungary and abroad alike. How do you see the position and role held by ELTE in Hungarian higher education and on the international scene?
ELTE is the country’s leading university playing a very important role in domestic higher education and is considered a prestigious research centre. It lives up to its old reputation and has excellent teachers, whose achievements are rightly famous around the world. It is a difficult situation, however, that many talented researchers are leaving the country, and although there may as well be counterexamples, many of them will never come back. It is becoming increasingly difficult to recruit new researchers.
In addition to doing research, you are also teaching at ELTE. How do you see the students today, and what are their career opportunities like?
What I have just said about researchers holds true for the students as well. Those who graduate here are well-prepared and can stand the competition with graduates from other universities. I find ELTE students brilliant: those who got a taste for maths at secondary school remain enthusiastic students here as well – and that is what makes teaching so rewarding.
The circulation in the world of scientists is increasing, and there are particularly numerous opportunities in Europe.
Today, it is no longer a problem for someone working abroad to contribute to mathematics teaching and research in Hungary, as well. Nevertheless, I am concerned that many people go abroad to study there right after secondary school. As a result, they have no contact with domestic research institutions and are less likely to come home. Those researchers who return to Hungary are motivated by the fact that there is a professional community to which it is worth coming home. If you ask me, I recommend that everyone should obtain at least their bachelor’s degree or even their master’s degree in this country, and then they can continue their studies somewhere else.
How do you see mathematics teaching in Hungary? What should be focused on during the teaching of mathematics, either in public education or in higher education?
Here, the teachers are more overwhelmed, and the students also have more lessons than the international average. This should be changed. I would also support developing a curriculum where the students were given more opportunities for independent work than presently. As far as I can see, in the field of Hungarian education, thinking in terms of longer-term projects and preparation for cooperation receives little weight in general, even though this is what increasingly promotes education and research.
In Europe, master’s programmes are often held in English. In the field of natural sciences, it might be worth switching to this. It would be advantageous if more foreigners came here to study for a couple of years. In my experience,
those students who attend the Budapest Semester talk about Hungary in a completely different way subsequently
and consider their relationship with Hungarian mathematics important. We should attract as many foreigners here as possible, not only students but also teachers.
Mathematics is considered a difficult subject. How could we tame this monster?
I can see two areas that could bring mathematics closer to students. One is the beauty, excitement, and intellectual challenge represented by mathematics. Many people understand this since they like playing chess and solving puzzles. There is a tradition of this in the teaching of mathematics in Hungary. It is enough to mention the book Playing with Infinity by Péter Rózsa.
To those less interested in why mathematics is beautiful, it can be demonstrated why it is useful and what can be achieved with it. They can be shown applications that demonstrate how they and their friends are affected by mathematical rules in their daily lives. What is the fastest way to get to school? Examples like this. (Of course, Google already tells this.) Such tasks may help overcome feelings of futility, boredom, and failure.
As president of the Hungarian Academy of Sciences, you launched a teaching research programme on the subject, which considerably enhanced the recognition of methodological research in the Hungarian and international scientific community. Why did you think this was important to do?
The development of education is extremely important, but it is rather neglected these days. Today, we tend to measure knowledge. PISA measures what someone has learnt, and we are normally not good at it. I would strongly support the establishment of a research institute that is engaged in how to teach certain fields of the discipline in an exciting way, how to use the Internet, what to do with the information explosion, and how to harmonize it with education. This is a long-term, ongoing task. I am certain that in five years, for example, the world will be completely different in terms of education. We have seen how the coronavirus pandemic has turned everything upside down in recent years. It is still unknown what effect the change in circumstances has had on young people: whether they acquired pieces of knowledge patched together or they learnt something new in the process.
This kind of continuous educational development cannot be implemented through applications for funding.
Scientific and non-scientific public life is dominated by the headway of artificial intelligence. What do you think about the role of this tool in mathematics?
In general, I regard it as a beneficial change that the applied fields of mathematics receive more attention and are less separated from basic research. Mathematics has become more appreciated due to the rapid development of computers, artificial intelligence, and biology. It is needed everywhere. For the time being, I cannot see how AI could do mathematical research on its own. A very important element of mathematical research is that we discover analogies between different fields and concepts, which lead to drawing a general conclusion or adapting a method in another field. This may produce significant results. We notice the analogies by chance, and AI could help with this maybe 15-20 years from now. It could also be used to scan and organise the excessive amount of studies published in this area of research.
Regarding machine learning, many people are wondering whether there is any point in thinking if the machine gives us the right answer.
Yes, indeed, this problem is often raised in connection with test exams, so we not only hold test exams in mathematics. It is difficult to assess knowledge in any case so that it would reveal whether someone understands what they have learnt, whether it has been integrated into their way of thinking. I don’t find assessment important, especially in other doctoral courses, because those who have made it this far are certainly able to learn things by themselves.
Why should I learn something when the machine tells me the answer? Every teacher is asked this question more and more often. In my opinion, if the machine solves many things, then more complex tasks can be given to it, and in such cases
the students need to learn which sub-tasks can be solved by simply reaching out to the machine.
As was the case with the calculator before. The students must realise, for example, that in the case of a complex operations research problem, the solution of a sub-problem is just a plain simplex algorithm.
What does mathematics offer today – including to other disciplines – that nothing else does?
It is often said that mathematics teaches a logical way of thinking. It is not taken seriously, even though it is still significant today. During the exams of first-year students, we can see that an elementary task where six or eight cases must be distinguished from each other proves to be difficult. In other words, this skill has not sufficiently developed from what the students learnt at secondary school.
In addition to logical thinking, I would also mention quantitative thinking. Without mathematics, we would not understand the acceleration of cars and other processes in physics, biological organisms, living creatures, living creatures making a forest, or the interaction of proteins in a cell. These are all intricate complex systems, grids, and basic structures where many things take place. Today, it is still unknown how DNA is able to encode the structure of the human brain. No matter how much information the DNA can store, it is not enough for this. Algorithms are constantly running in and around us, information flows through neural pathways and chemical channels.
These processes must now be understood in such details as we once understood the movements of the planets.
A new system of concepts is required for their understanding. This is a major challenge for the future, and mathematics can prove useful in this.
What example would you set for young people today? How they can succeed?
I would tell them that things are worth thinking about. When they come across a mathematical phenomenon that is regarded as a hoary chestnut, they should remember that it is not. We know particularly little about more recent phenomena. For example, during the coronavirus pandemic, it turned out in connection with the mathematics of epidemics how little we know about even very simple models to be able to make predictions. If you cannot understand something, start thinking about it. It doesn’t even matter if you don’t make a discovery. That’s also part of a researcher’s career.